Local instabilities in magnetized rotational flows: a short-wavelength approach

• Published in: Journal of fluid mechanics Vol. 760; pp. 591 - 633
• Main Authors: Kirillov, O. N., Stefani, F., Fukumoto, Y.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.12.2014
• Subjects: Accretion; Accretion disks; Approximation; Earth, ocean, space; Exact sciences and technology; External geophysics; Fluid dynamics; Fluid flow; Frameworks; Fundamental areas of phenomenology (including applications); Geophysics. Techniques, methods, instrumentation and models; Instability; Magnetic field; Magnetic fields; Magnetic resonance imaging; Magnetohydrodynamics; Magnetohydrodynamics and electrohydrodynamics; Metals; Physics; Profiles; Reynolds number; Rotation; Stability; Stability analysis; Valuation methods; Wavelength; geophysical and geological flows; instability; MHD and electrohydrodynamics; Astrophysical fluid dynamics; MHD flow; Approximation; Astrophysics; Dispersion relations; Hydrodynamic instability; Liquid metals; Magnetic fields; Rotational flow; Geophysical fluid dynamics; Viscous fluids
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2014.614

We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, helical and azimuthal version of the magnetorotational instability (MRI), as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies e.g. to liquid-metal experiments but also to the colder parts of accretion disks. We show that the inductionless versions of MRI that were previously thought to be restricted to comparatively steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its current-free (in the fluid) profile. We find an explicit criterion separating the pure azimuthal inductionless MRI from the regime where this instability is mixed with the Tayler instability. We further demonstrate that for particular parameter configurations the azimuthal MRI originates as a result of a dissipation-induced instability of Chandrasekhar’s equipartition solution of ideal magnetohydrodynamics.